In photolithography operations which are important steps in the fabrication of semiconductor devices, optical masks are used typically to pattern a photoresist layer. With the design of semiconductor devices becoming increasingly more complicated in design and finer in dimensions, we are also seeing a trend of more radical departure in their layouts from the traditional, and more or less, symmetric, design. It has become not-all-too-uncommon to have semiconductor wafer layouts, and thus the associated optical masks, that involve strong variations in the first direction (say, x-direction), but relatively slow variations in the second direction (say, y-direction), creating an asymmetric optical mask system.
In a typical masked photo exposure operation, a coherent light (typically a KrF laser light passed through a condensing lens) is emitted upon the optical mask at an inclined angle. Two high frequency light beams and one direct light beam will be generated as a result of diffraction from the optical mask. The direct light beam is a relatively low frequency 0th-order diffracted light and the two relatively high frequency high beams are 1 st-order diffracted light beams. When the diffraction angle exceeds a certain value, the high frequency portion of the light beams may be diffracted outside the area of the objective lens disposed behind the optical mask, resulting in a substantial loss in the optical resolution, particularly in the x-direction, where variations are stronger. (It should be noted that designation of x- and y-directions are only arbitrary.) This can adversely affect the precision and sometimes the acceptability of the resultant semiconductor device.
In other words, because of the asymmetry in the variations of the pattern of the optical mask between the x- and y-directions, different bandwidths exist, and the pertinent bandwidths (i.e., the two-dimensional bandwidth distribution) occupy a two-dimensional cigar-shaped area in the transformed F.sub.x -F.sub.y frequency domain as shown in FIG. 1. As a result, in order to improve semiconductor quality and maintain good production yield, it is important to research various ways that may reduce the asymmetry of the frequency domain.